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Although possible worlds semantics is a powerful tool to represent the semantic properties of natural language sentences, it has been often argued that it is too coarse: with the tools that possible worlds semantics puts at our disposal, any relevant semantic difference has to be a truth conditional difference representable as a difference in intension. A case that raises questions about the ability of possible worlds semantics to make the appropriate discriminations is the distinction between rigidity and direct reference, an issue deeply connected to the representation of the behaviour of two operators: ‘dthat’ and ‘actually’. Differences between the mode of operation of ‘dthat’ and ‘actually’ have been observed, but they have not been examined in depth. Our purpose is to explore systematically to what extent the observed differences between the two operators have truth conditional consequences that are formally representable in possible worlds semantics.

On ‘actually’ and ‘dthat’: Truth-conditional Differences in Possible Worlds Semantics